The self-similar solution for draining in the thin film equation

G.J.B. van den Berg; M. Bowen; J.R. King; M.M.A. El-Sheikh

doi:10.1017/S0956792504005510

The self-similar solution for draining in the thin film equation

G.J.B. van den Berg, M. Bowen, J.R. King, M.M.A. El-Sheikh

Mathematics

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Abstract

We investigate self-similar solutions of the thin film equation in the case of zero contact angle boundary conditions on a finite domain. We prove existence and uniqueness of such a solution and determine the asymptotic behaviour as the exponent in the equation approaches the critical value at which zero contact angle boundary conditions become untenable. Numerical and power-series solutions are also presented.

Original language	English
Pages (from-to)	329-346
Journal	European Journal of Applied Mathematics
Volume	15
Issue number	3
DOIs	https://doi.org/10.1017/S0956792504005510
Publication status	Published - 2004

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MR2092917

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10.1017/S0956792504005510

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title = "The self-similar solution for draining in the thin film equation",

abstract = "We investigate self-similar solutions of the thin film equation in the case of zero contact angle boundary conditions on a finite domain. We prove existence and uniqueness of such a solution and determine the asymptotic behaviour as the exponent in the equation approaches the critical value at which zero contact angle boundary conditions become untenable. Numerical and power-series solutions are also presented.",

author = "{van den Berg}, G.J.B. and M. Bowen and J.R. King and M.M.A. El-Sheikh",

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T1 - The self-similar solution for draining in the thin film equation

AU - van den Berg, G.J.B.

AU - Bowen, M.

AU - King, J.R.

AU - El-Sheikh, M.M.A.

N1 - MR2092917

PY - 2004

Y1 - 2004

N2 - We investigate self-similar solutions of the thin film equation in the case of zero contact angle boundary conditions on a finite domain. We prove existence and uniqueness of such a solution and determine the asymptotic behaviour as the exponent in the equation approaches the critical value at which zero contact angle boundary conditions become untenable. Numerical and power-series solutions are also presented.

AB - We investigate self-similar solutions of the thin film equation in the case of zero contact angle boundary conditions on a finite domain. We prove existence and uniqueness of such a solution and determine the asymptotic behaviour as the exponent in the equation approaches the critical value at which zero contact angle boundary conditions become untenable. Numerical and power-series solutions are also presented.

U2 - 10.1017/S0956792504005510

DO - 10.1017/S0956792504005510

M3 - Article

SN - 0956-7925

VL - 15

SP - 329

EP - 346

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

IS - 3

ER -

The self-similar solution for draining in the thin film equation

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